Wafer Residency Time Constraints Research Articles

Virtual Cell-Based Scheduling Approach to Single-Robotic-Arm Cluster Tools Subject to Wafer Residency Time Constraints

Virtual Cell-Based Scheduling Approach to Single-Robotic-Arm Cluster Tools Subject to Wafer Residency Time Constraints

Scheduling a Single-Arm Two-Cluster Tool With a Process Module Failure Subject to Wafer Residency Time Constraints

Multi-cluster tools are widely adopted in semiconductor manufacturing. When a process module (PM) at a step fails, a multi-cluster tool cannot complete the process recipe of work-in-process wafers and must be forced to enter a closedown process to be empty. To increase the throughput of a wafer fab, it is economically significant to shorten the failure-closedown process. However, due to the wafer residency time constraints, it is highly challenging to respond to a PM failure and find a corresponding optimal schedule. By assuming no parallel PM at a step, this work is the first to study this important issue for scheduling multi-cluster tools. We analyze the task sequences and synchronization conditions for robot activities to avoid deadlock in a shared buffer module. Upon these analyses, for process-dominant multi-cluster tools whose optimal steady-state schedule is known, algorithms are proposed to synthesize the proper sequences for robots in case of PM failures, then, a nonlinear program model is proposed to find an optimal schedule for the corresponding closedown process or decide no feasible solutions. The proposed model can uniformly deal with different scenarios of PM failures. Examples are given to illustrate the application of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In a wafer fab, there are hundreds, even thousands, of cluster tools. It is common that a failure of a processing module happens in a cluster tool. How to intelligently respond to such a random failure in a multi-cluster tool is an important issue in real-world production. This paper studies the scheduling problem of a multi-cluster tool in case of a failure at a PM. For a multi-cluster tool in case of a failure module, the proposed method can significantly reduce the loss of work-in-process wafers and shorten the closedown process.

Dual-Arm Cluster Tool Scheduling for Reentrant Wafer Flows

Cluster tools are the key equipment in semiconductor manufacturing systems. They have been widely adopted for many wafer fabrication processes, such as chemical and physical vapor deposition processes. Reentrant wafer flows are commonly seen in cluster tool operations for deposition processes. It is very complicated to schedule cluster tools with reentrant processes. For a dual-arm cluster tool with two-time reentering, the existing studies point out that a one-wafer periodical (1-WP) schedule can be found, and it is optimal in terms of productivity. However, for some wafer fabrication processes, wafers should be processed at some PMs more than two times. This gives rise to a question of whether there still exists a 1-WP schedule for dual-arm cluster tools with the number of reentering times being more than two such that the cycle time of a tool can reach the lower bound. This problem is still open, and this is what this work wants to tackle. For a dual-arm cluster tool with the number of reentering times being k (&gt;2) times, if there does not exist a value f ∈ {1, 2 …} such that k = 3f, theoretical proofs are given to show that a 1-WP schedule can be found, otherwise it does not exist. For cases with a 1-WP schedule, the cycle time can be obtained by analytical expressions. For the cases without a 1-WP schedule, two new methods for a three-wafer periodical schedule are proposed to improve the system productivity by comparing it with an existing three-wafer periodical schedule. The applications of the obtained results are demonstrated by examples. Wafer residency time constraints are required for some wafer fabrication processes. Note that the results obtained in this work cannot be directly applied to cluster tools with both reentrant wafer flows and wafer residency time constraints. Nevertheless, schedulablity and scheduling analyses for that applications can be conducted based on the obtained results in this work.

Influence of Dynamic Accuracy Constraints of Manipulator of Wafer Transmission Robot on Scheduling and Control of Single-Armed Cluster Tools

The wafer transfer robot is a key part of integrated circuit equipment which performs the transit of wafers precisely, quickly and steadily. The dynamic accuracy of the manipulator of the wafer transfer robot directly affects the quality of transferring and processing wafers and even the scheduling and control of the cluster tools. Thus, it is essential to study the influence of the dynamic accuracy of the manipulator of wafer transmission robots on the scheduling and control of cluster tools. In this paper, single-arm cluster tools are taken as the research object. The horizontal torsional vibration equations of the manipulator of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R$ </tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta $ </tex-math></inline-formula> robot are constructed, and the torsional vibration attenuation characteristics of the manipulator are analyzed. Based on the torsional vibration equations, the intrinsic relationships between the dynamic accuracy of the manipulator and the waiting times of the manipulator are explored when the manipulator loads and unloads the wafers. Then the two-stage approach is proposed for the scheduling and control of single-arm cluster tools. The first stage determines the minimum waiting times of the manipulator according to the intrinsic relationships between the dynamic accuracy of the manipulator and the waiting times of the manipulator when the manipulator is waiting for loading and unloading wafers in each processing module and load lock. The second stage achieves the scheduling optimization and control of single-arm cluster tools with dynamic accuracy constraints and wafer residency time constraints by establishing a mathematical programming model for the scheduling and control of single-arm cluster tools. Finally, illustrative examples are presented to analyze the influence of the dynamic accuracy of the manipulator on the scheduling and control of single-arm cluster tools.

Scheduling of time-constrained single-arm cluster tools with purge operations in wafer fabrications

Purge operations are widely used to remove residual chemicals and impurities in chambers of wafer fabrication systems to ensure wafer quality. However, such operations lead to more start-up transient processes and wafer delays. In addition, wafer residency time constraints must be met to ensure the wafer quality. Thus, the system scheduling problem with such considerations will become more complicated. This work aims to optimize the start-up transient process of a single-arm cluster tool with purge operations and wafer residency time constraints by using resource-oriented Petri net (ROPN) models. Based on the models, we dynamically depict the behavior of the steady state and start-up transient processes of a single-arm cluster tool with purge operations. Then, a scheduling method that dynamically adjusts the robot waiting time is proposed to find an optimal schedule for such systems with purge operations and wafer residency time constraints. Finally, some examples are tested to illustrate the effectiveness of our method.

An Efficient Binary Integer Programming Model for Residency Time-Constrained Cluster Tools With Chamber Cleaning Requirements

Cluster tools play a significant role in the entire process of wafer fabrication. As the width of circuits in semiconductor chips shrinks down to less than 10nm, strict operational constraints are imposed on the operations of cluster tools in order to ensure the quality of processed wafers. Particularly, wafer residency time constraints and chamber cleaning requirements are commonly seen in etching, chemical vapor deposition, coating processes, etc. They make the scheduling problem of cluster tools more challenging. This work aims to provide a solution for dual-arm cluster tools with wafer residency time constraints and chamber cleaning requirements. To do so, it proposes a novel virtual wafer-based scheduling method. By this method, under a steady state, a PM processes either a real or virtual wafer at a time. When a PM processes a virtual one, its chamber can perform a cleaning operation. In this way, we can meet not only the strict residency time constraints for real wafers, but also innovatively meet chamber cleaning requirements. Based on such a novel scheduling method, an efficient binary integer programming model is established to optimize the throughput of cluster tools. Finally, experiments are performed to show the efficiency and effectiveness of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —To ensure wafer quality in semiconductor manufacturing, engineers have to impose wafer residency time constraints and chamber cleaning requirements on the operations of cluster tools. In order to tackle their scheduling problem with these constraints, this work proposes a novel method based on the use of virtual wafers. Under a one-cyclic schedule obtained for time-constrained cluster tools without chamber cleaning requirements, virtual wafers are loaded into the tool such that when a PM processes a virtual wafer, a chamber cleaning operation can be performed in practice. The key to solve this scheduling problem is to find a wafer loading sequence with the highest performance in terms of cycle time. To do so, this work establishes an efficient binary integer programming model to search for such a solution. Since the obtained solution is a periodical wafer loading sequence based on a one-wafer cyclic schedule, it can be easily implemented. Therefore, this work has a high practical value to numerous semiconductor manufacturers.

Optimally Scheduling Dual-Arm Multi-Cluster Tools to Process Two Wafer Types

To satisfy the requirements of high-mix integrated-circuit chip production, multiple wafer types are grouped into a lot to be fabricated concurrently in a multi-cluster tool system. However, the existing studies do not solve the scheduling problem of multi-cluster tools with multiple wafer types being processed and wafer residency time constraints being imposed. This study aims to find a feasible steady-state schedule for a process-dominant multi-cluster tool that processes two wafer types concurrently. A novel robot cycle, called one-wafer-per-type cycle, and a two-swap robot sequence are defined, under which the minimal cycle time can be achieved. Further, the schedulability for individual cluster tools with two wafer types is proved upon closed-form derivations. The schedulability conditions of a one-wafer-per-type schedule for the system are proposed. With such conditions, an efficient algorithm is established to obtain a schedule in a two-swap sequence. Several instances show the application and effectiveness of the proposed method.

Green scheduling of dual-armed cluster tool based on cleaning scenarios

Semiconductor manufacturing is one of the most complex manufacturing systems, of which wafer fabrication is the core part. Dual-armed cluster tool is widely used in the wafer manufacturing industry with its efficient production characteristics. The scheduling process of the dual-armed cluster tool has to consider many constraints; wafer residency time constraints, activity time fluctuations, etc. are relatively basic requirements. With the improvement of wafer processing accuracy in the market, green scheduling and processing efficiency are emerging as key issues for research, the scheduling of dual-armed cluster tool considering the above constraints is an NP-hard problem. Based on this study, the clean scenario is divided, a scheduling model that can realize low-carbon production is constructed, and the scheduling idea of the dual-armed cluster tool under clean transient is analyzed to ensure that the clustering tool is in green scheduling and restored to a steady state as soon as possible during the scheduling process.

Scheduling of Single-Arm Cluster Tools with Residency Time Constraints and Chamber Cleaning Operations

To ensure wafer quality, engineers have to impose wafer residency time constraints and chamber cleaning operations on cluster tools; this has been widely used in semiconductor manufacturing. Wafer residency time constraints and chamber cleaning operations make the scheduling problem of cluster tools more challenging. This work aims to solve such a scheduling problem for single-arm cluster tools and presents a novel method based on the use of virtual wafers. Under a one-cyclic schedule obtained for single-arm cluster tools without chamber cleaning requirements, virtual wafers are loaded into the tool such that when a process module (PM) processes virtual wafers, a chamber cleaning operation is performed in practice. The key to solve this scheduling problem is to find a wafer loading sequence with the highest performance in terms of cycle time. With this idea, this work constructs a genetic algorithm to search for such a solution. Since the obtained solution is a periodical wafer loading sequence based on a one-wafer cyclic schedule, it can be easily implemented. Therefore, this work has high practical value to numerous semiconductor manufacturers. Experiments were performed to show the efficiency and effectiveness of the proposed method.

Efficient Approach to Failure Response of Process Module in Dual-Arm Cluster Tools With Wafer Residency Time Constraints

In semiconductor manufacturing, a process module (PM) failure in cluster tools (CTs) happens from time to time. To effectively operate a CT, such a failure should be handled in a proper and timely manner. This issue becomes much more complicated because wafer residency time constraints (WRTCs) must be met to ensure the quality for some wafer fabrication processes. With such constraints, if a tool is operated under a periodic schedule and a PM fails, it is desired that the tool can still operate under a periodic schedule if it is possible. Nevertheless, the periodic schedule after a PM failure must be different from that before its failure since in this case the tool is degraded. Thus, there must be a transient process between them. It is a great challenge to operate a tool such that it can go through such a transient process with WRTCs being always satisfied. This paper aims to solve this problem by proposing PM failure response policies which can successfully transfer a CT to the feasible schedule after failure from the one before a failure. Then, efficient algorithms are developed to improve these response policies. The proposed policies are composed of simple control laws such that they can be realized in real time and online. Illustrative examples are presented to show their applications.

Efficient Approach to Scheduling of Transient Processes for Time-Constrained Single-Arm Cluster Tools With Parallel Chambers

In wafer manufacturing, extensive research on the operations of cluster tools under the steady state has been reported. However, with the shrinking down of wafer lot size, such tools are frequently required to switch from handling one lot of wafers to another, resulting in more transient processes, including start-up and close-down ones. Also, wafer residency time constraint is critical for many wafer fabrication processes. To cope with the transient scheduling problem of time-constrained single-arm cluster tools with parallel chambers, based on a generalized backward strategy, this paper first builds timed Petri net models for these two transient processes. Then, two linear programs are derived for the first time to search a feasible schedule with a minimal makespan. Two industrial examples are given to demonstrate the effectiveness of the obtained results at last.

Modeling and Optimal Cyclic Scheduling of Time-Constrained Single-Robot-Arm Cluster Tools via Petri Nets and Linear Programming

Scheduling a cluster tool with wafer residency time constraints is challenging and important in wafer manufacturing. With a backward strategy, the scheduling problem of such single-robot-arm cluster tools is well-studied in the literature. It is much more challenging to schedule a more general case whose optimal scheduling strategy is not limited to the backward one. This work uses a timed Petri net (PN) to model the dynamic behavior of the system and presents a method to determine the optimal scheduling strategy for the system. Based on its PN model and the obtained strategy, it reveals that the key issue to schedule such a tool is to determine when and how long the robot should wait for. Based on this finding, this work establishes for the first time the necessary and sufficient conditions regarding the existence of an optimal and feasible one-wafer cyclic schedule for single-robot-arm cluster tools. It then formulates a computationally efficient linear program to find it if existing, and finally gives industrial examples to show the application and power of the proposed method.

Post-processing time-aware optimal scheduling of single robotic cluster tools

Integrated circuit chips are produced on silicon wafers. Robotic cluster tools are widely used since they provide a reconfigurable and efficient environment for most wafer fabrication processes. Recent advances in new semiconductor materials bring about new functionality for integrated circuits. After a wafer is processed in a processing chamber, the wafer should be removed from there as fast as possible to guarantee its high-quality integrated circuits. Meanwhile, maximization of the throughput of robotic cluster tools is desired. This work aims to perform post-processing time-aware scheduling for such tools subject to wafer residency time constraints. To do so, closed-form expression algorithms are derived to compute robot waiting time accurately upon the analysis of particular events of robot waiting for single-arm cluster tools. Examples are given to show the application and effectiveness of the proposed algorithms.

Wafer sojourn time fluctuation analysis for time-constrained dual-arm multi-cluster tools with activity time variation

ABSTRACT In semiconductor manufacturing systems, a time-constrained multi-cluster tool should be scheduled such that a wafer stays in a process chamber in a given time range to satisfy a wafer residency time constraint. In practice, activity time is subject to variation. It could lead to some fluctuation of wafer residency time in a process chamber. Hence, it is crucial to analyze how wafer residency time varies with activity time variation. This issue is especially challenging for multi-cluster tools. This work focuses on determining the exact upper bound of wafer sojourn time delay resulted from activity time variation for dual-arm multi-cluster tools. After discussing their dynamic behaviours, it presents a two-level real-time operational architecture and a real-time control policy. Based on them, this work derives for the first time an efficient algorithm to calculate the exact upper bound of wafer sojourn time delay in a process chamber. As a result, engineers can test whether a given schedule is feasible. Several examples of industrial significance are used to demonstrate the application of the proposed approach.

Closing-Down Optimization for Single-Arm Cluster Tools Subject to Wafer Residency Time Constraints

A kind of facilities for wafer fabrication, cluster tools (CTs) need to close down to an idle state from time to time because of periodical maintenance and switches from one type of lots to another, which is called a normal close-down process (NCDP). It is crucial to optimize such a transient process since it tends to occur more and more frequently due to customization. Also, process modules (PMs) in CTs are known to be failure-prone. Once a PM failure occurs, a tool needs to close down to an idle state as well, which is different from NCDP and is called a failure close-down process (FCDP). With wafer residency time constraints (WRTCs) being imposed, close-down process optimization for such a tool is challenging, since one needs to not only finish this process as soon as possible but also meet WRTCs during this transient process. In order to tackle this problem, this article first introduces steady state scheduling problems. Then, with a presented backward robot task sequence, a linear programming model is first proposed to optimize NCDP. To deal with the PM failures, efficient PM failure response policies are formulated for the cases in which a PM fails. Then, four linear programs are proposed to optimize an FCDP. Finally, industrial case studies are given to show the usefulness of the proposed approaches.

Multiobjective Scheduling of Dual-Blade Robotic Cells in Wafer Fabrication

As a kind of robotic cells, cluster tools are widely used for semiconductor wafer fabrication processes since they provide a reconfigurable and efficient environment. With recent advances in new semiconductor materials, the circuit line width has continuously being shrunk down, which brings new challenges for manufacturers. They require that a wafer should be moved away from a processing chamber as soon as possible after its processing is finished. To ensure high-quality integrated circuits in a wafer, its post-processing residency time must be minimized. It is also highly desirable to maximize the throughput of robotic cluster tools. This article aims at scheduling such tools with multiple objectives subject to wafer residency time constraints. To do so, new algorithms are proposed to calculate robot waiting time delicately upon the analysis of particular events of robot waiting for dual-blade robotic tools and optimally schedule such tools. The numerical results of industrial examples show that the proposed algorithms can provide an effective method to find schedules for dual-blade cluster tools such that multiple objectives are optimized.

Efficient Approach to Cyclic Scheduling of Single-Arm Cluster Tools With Chamber Cleaning Operations and Wafer Residency Time Constraint

In semiconductor manufacturing, with the shrinking down of wafer circuit widths, a strict quality control is required for wafer fabrication processes, resulting in that after a wafer being processed and removed from a chamber, a cleaning operation that takes significant time is performed for eliminating the chemical residual. Such a cleaning operation makes a traditional backward strategy for single-arm cluster tools inefficient. By the existing studies, it is shown that the productivity can be improved if some numbers of chambers at a step are kept empty. With this idea, an extended backward strategy is proposed by deciding the optimal number of empty chambers. Based on such a strategy, this paper studies the challenging problem for scheduling a single-arm cluster tool with both chamber cleaning operations and wafer residency time constraint for the first time. By building a timed Petri net model for the system, two linear programs are proposed to determine the minimal cycle time and test the existence of a feasible schedule and find it if existing. At last, two industrial examples are used to demonstrate the obtained results.

Scheduling Cluster Tools in Semiconductor Manufacturing: Recent Advances and Challenges

Cluster tools are automated robotic manufacturing systems containing multiple computer-controlled process modules. They have been increasingly used for wafer fabrication. This paper reviews the modeling and scheduling methods for cluster tools with both nonrevisiting and revisiting processes. For nonrevisiting processes, we focus on the modeling and scheduling problems of cluster tools with different constraints. Then, their solution methods are reviewed and compared. For revisiting processes, this paper first discusses the scheduling problem of some general manufacturing systems with revisiting. Then, the modeling and scheduling methodologies used to solve the scheduling problems of cluster tools with revisiting processes are reviewed. Future research directions and conclusions are finally discussed. Note to Practitioners —Semiconductor manufacturing systems are among the most advanced and complicated manufacturing systems. Their key equipment is highly automated robot-based cluster tools. With wafer residency time constraints, wafer revisiting, activity time variation, chamber cleaning requirements, and failure-prone process modules (PMs), it is very challenging to schedule and control them. This paper surveys their modeling and scheduling methods. Scheduling them requires one to schedule their robot tasks and processing activities simultaneously. Owing to wafer residency time constraints and the lack of buffers among PMs, it is difficult to conduct their optimal scheduling. This paper presents a thorough review of the state-of-the-art research results about modeling and optimal scheduling of clusters tools and indicates the future research directions.

Wafer Sojourn Time Fluctuation Analysis of Time-Constrained Dual-Arm Cluster Tools With Wafer Revisiting and Activity Time Variation

A robotic cluster tool involves many activities whose time is subject to some disturbance, thus leading to the activity time variation. It results in wafer sojourn time fluctuation in a process module, which may in turn violate wafer residency time constraints. Some wafer fabrication requires a revisiting process. With wafer revisiting, the effect of activity time variation on wafer sojourn time fluctuation is so complicated that no analysis was reported to the best knowledge of the authors. It is vitally important to accurately analyze it. To do so, this paper adopts a Petri net model to describe the dynamical behavior of cluster tools. With this model, a real-time control policy is proposed to offset the effect of the activity time variation on wafer sojourn time fluctuation as much as possible. Then, the wafer sojourn time delay is analyzed and algorithms are developed to calculate its exact upper bound. With the proposed method, one can check if a given schedule is feasible under bounded activity time variation. Some practical examples are given to show the application of the proposed approach.

Petri Net Modeling and Scheduling of a Close-Down Process for Time-Constrained Single-Arm Cluster Tools

In wafer fabrication, a robotic cluster tool is required to be closed down in order for engineers to perform its on-demand and preventive maintenance and switch between different wafer lots. They often deal with a close-down process subject to wafer residency time constraints, i.e., a wafer must exit from a processing chamber before its quality degradation within a certain time limit. To obtain higher yield, it is very important to optimize a close-down process for a cluster tool. Yet the existing literature pays no or little attention to this issue. By focusing on a time-constrained single-arm cluster tool, this paper intends: 1) to build its Petri net model to analyze its schedulability and 2) to develop computationally efficient algorithms to find an optimal and feasible schedule for its closing-down process under different workloads at its steps. Industrial examples are used to illustrate the application of the proposed method.